Different from a conventional imaging lens, a Fourier lens may exhibit, on a spectrum plane thereof, an intensity distribution assuming a linear relationship with the spatial frequency of incident light, and it has important applications in many fields, such as spatial light filtering, holography, information processing, compressed sensing and high-resolution imaging.
Spatial spectrum distortion means that there is a difference between the ideal and practical positions of the light spot, on a back focal plane of a Fourier lens, of parallel light rays incident onto the Fourier lens. In order to guarantee accurate spatial spectrum distribution, it is necessary to make the Fourier lens produce a distortion value having an equal magnitude but an opposite sign to the nonlinear error value of a spectral point. If the lens is not subject to aberration correction in an ordinary way, with appropriate distortion retained but with spherical aberration and coma aberration of the lens eliminated, then emergent light rays are required to meet the Abbe sine condition. As can be known from the aberration theory, in the process of eliminating the spherical aberration and coma aberration of the lens, a certain amount of distortion will inevitably be left. In the prior art, a lens made of a continuous medium (such as glass or other transparent mediums) are used, such that the aberration caused by the amount of distortion is compensated by making the lens have different thicknesses at different regions.
Since the aberration of the Fourier lens is compensated by making the lens have different thicknesses at different regions in the prior art, such a design essentially relies on the phase difference accumulated during the propagation of light rays in the medium, which belongs to the scope of geometrical optics. As a result, the working angle of the existing Fourier lens still needs to meet the paraxial condition (which generally requires the angle not to be larger than 30°), that is, the range of the working angle is small.